It's not doctoral stuff, but a reasonable model would be a high-end undergraduate problem. Consider thirty uniform physical pendula arranged in a line, each rigidly fixed at the top, linked with a horizontal low-constant spring to the next one midway up. The tops of the pendula are subjected to a sinusoidal horizontal driving force.

We need to add damping.

George - could that be solved without differential equations? I doubt it.

Now, to similate the fore-and-aft motion of the legs, rigidly fix out-of-phase sinusoidal fore-and-aft drivers to the end pendula. These have the same/opposite phase as the top driver. Now we have a real challenge.